408 Life and Letters of Francu Calton 



Those who recognise the relative mercy of the long drop may wonder why 

 Ciipital punishment has not been still further modified m the direction of 

 sciircely less painful, but more seemly, methods of dis]x>sing of the socially 

 abhorrent. 



Galt<in further contributed a letter to the discussion on "Corporal Punish 

 ment " which developed in the Times in 1898. He considered that the writers 

 on the subject had overlooked two important points: 



"The first is, the worse the criminal the less sensitive he is to pain, the correlation between 

 the bluntneas of the moral fwlinpH and those of the IjoHily sensations being very ninrkotl. The 

 Moond relates to the connection Ix'tween the force of the blow and the pain it occasions, which 

 do not vary at the sanu! rat<', hut approximately, according to Weber's law, four times as heavy 

 a blow <mly producing alxiut twice as much pain. In a Utopia the business of the .ludge woul<i 

 be confined t-o s<'ntcncing the criminal to so many units of pain in such and such a form, leaving 

 it to anthropologists skilled in that branch of their science to make preliminary experiments 

 and to work out tables to determine the amount of whipping or whatever it might be thai 

 would produce the desired results. Really these latter considerations might even now be madi' 

 the subject of a solid scientific paper of no small interest, but they cannot be more than hinted 

 kt in a short letter like this, which has to be written in non-technical language." 



The unit of pain — quite apart from corporal j)unishment — .seem.s no more 

 incapable of measurement than a unit of intelligence. The threshold of the 

 sensation of pain might be determined in a number of ways, and then corre- 

 lated with other mental and physical characters of the individual. Like all 

 Galton's writings, this brief letter suggests unexhausted fields for the per- 

 sistent and cautious investigator. 



Galton's fertility of statistical ideas may be further illustrated by two 

 papei-s, one belonging to 1804 when he was seventy-two years of age, and 

 the other written fifteen years later when he was 87. The first was contri- 

 buted to the Proceetfi'yu/s of the Roi/cd Society^ and deals with the import.inl 

 j)roblem of the fertility of marriages according to the ages of father and 

 mother. The fertility is measured by percentage of families which have a 

 child when the husband and wife are of the given ages. If a chart be formed 

 of which one variate is age of father, the second age of mother, and the 

 percental offspring be inscribed for each pair of ages, then Galton proposes to 

 represent the loot of equal percentages by contours, which he terms isogtms. 

 By a fairly simple, if somewhat rough process he constructs these isogens 

 for Korosi s Budapest data, and we reproduce them below. 



The diagram indicates that the form of the isogens its long as the husband 

 is older than the wife is very closely a system of straight equidistant and 

 diagonal lines. As a result of this Galton concludes that the fertility of a 

 husband of age a„ and a wife of age a» will be closely given by 



p = 9S — a„ — a^, 



provided that (i) the wife is not older than the husband, and (ii) she is not 

 less than 23 nor (iii) more than 40 years of age. 



' Vol. LV, pp. 18-23. "Results derived from the Natality Table of Korosi by employing 

 ihr- method of Contours or Isogens." 



